The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction governs the coupling between localized spins and is strongly affected by the environment in which these spins reside. In superconductors, this interaction becomes long-ranged and provides information about the orbital symmetry of the superconducting order parameter. In this work, we consider the RKKY interaction between localized spins mediated by $p$-wave triplet superconductors. In contrast to the well-studied RKKY interaction in $d$-wave superconductors, we find that the spin of the Cooper pair in a triplet state also modulates the spin-spin coupling. We consider several different types of $p$-wave triplet states and find that the form of the RKKY interaction changes significantly with the symmetries of the order parameter. For nonunitary superconducting states, two new terms appear in the RKKY interaction: a background spin magnetization coupling to the individual spins and, more interestingly, an effective Dzyaloshinskii-Moriya term. The latter term oscillates with the separation distance between the impurity spins. Finally, we find that the finite spin expectation value in nonunitary superconductors in concert with the conventional RKKY interaction can lead to noncollinear magnetic ground states even when the Dzyaloshinskii-Moriya term is negligible. The RKKY interaction in $p$-wave triplet superconductors thus offers a way to achieve new ground state spin configurations of impurity spins and simultaneously provides information about the underlying superconducting state.

Within the variational polaron equation framework, the Fröhlich model for cubic systems with threefold degenerate electronic bands is numerically solved in the strong-coupling regime for a wide range of its input parameters. By comparing the results to the previously reported ones obtained with the Gaussian ansatz approach, the inadequacy of the latter is uncovered, especially when degenerate bands are present in a system. Moreover, the symmetry groups of polaronic solutions in the cubic generalized Fröhlich model without spin-orbit coupling are investigated: We provide and discuss a phase diagram of symmetry groups of ground-state polarons, showing spontaneous symmetry breaking. While the cubic symmetry of the three-band degenerate model Hamiltonian corresponds to the full octahedral group $O_h$, lowest-energy polarons possess either $D_{4h}$ or $D_{3d}$ point groups. This phase diagram bears some similarities but differs nevertheless from the one that is obtained by the straight analysis of the band effective masses. The obtained results will provide a firm ground for further exploration of the generalized Fröhlich model and will likely be applicable beyond the model's inherent approximations.

Magnonic waveguides based on magnetic domain walls surpass conventional magnonic waveguides, which typically feature single magnetic domains, in nearly all critical aspects. Consequently, they are considered pivotal for the development of future nanomagnonic circuits. A distinctive feature of these waveguides is the complete absence of a bandgap, known as the vanishing magnon barrier. This feature is of great theoretical importance and has practical relevance for several applications, but it has received limited attention thus far. In our research, we employ micromagnetic simulations to investigate the spin-wave propagation in a domain-wall based magnonic waveguide, which includes reconfigurable periodic modulations. The magnonic band structure within the domain-wall waveguide can be significantly altered based on the magnetization configuration of the modulating magnets, resulting in the creation of bandgaps or leaving the structure unchanged, as though no modulation were applied. The bandgaps arise from the Bragg reflection of spin waves due to an induced periodic potential. A resonance-enhanced propagation state of the waveguide and modulation magnets, indicative of mode matching, results in the emergence of an allowed band within each bandgap under specific conditions. This study may open an effective route to control the band structure of domain-wall waveguides.

An important open puzzle in the superconductivity of ${\mathrm{UTe}}_2$ is the emergence of broken time reversal superconductivity from a nonmagnetic normal state. Breaking time reversal symmetry in a single second-order superconducting transition requires the existence of two degenerate superconducting order parameters, which is not natural for orthorhombic ${\mathrm{UTe}}_2$. Moreover, experiments under pressure [D. Braithwaite et al., Commun. Phys. 2, 147 (2019)] suggest that superconductivity sets in at a single transition temperature in a finite parameter window, in contrast to the splitting between the symmetry-breaking temperatures expected for accidental degenerate orders. Motivated by these observations, we propose a mechanism for the emergence of broken time reversal superconductivity without accidental or symmetry-enforced order-parameter degeneracies in systems close to a magnetic phase transition. We demonstrate using Landau theory that a cubic coupling between proximate magnetic order and magnetic moments of Cooper pairs (pair Kondo coupling) can drive time reversal symmetry-breaking superconductivity that onsets in a single, weakly first-order transition over an extended region of the phase diagram. We discuss the experimental signatures of such transition in thermodynamic and resonant ultrasound measurements. A microscopic origin of pair Kondo coupling is identified as screening of magnetic moments by chiral Cooper pairs, built out of two nondegenerate order parameters, an extension of Kondo screening to unconventional pairs.

Magic-angle twisted bilayer graphene (MATBG) has been extensively explored both theoretically and experimentally as a suitable platform for a rich and tunable phase diagram that includes ferromagnetism, charge order, broken symmetries, and unconventional superconductivity. In this paper, we investigate the intricate interplay between long-range electron-electron interactions, spin fluctuations, and superconductivity in MATBG. By employing a low-energy model for MATBG that captures the correct shape of the flat bands, we explore the effects of short- and long-range interactions on spin fluctuations and their impact on the superconducting (SC) pairing vertex in the matrix random phase approximation (matrix RPA). We find that the SC state is notably influenced by the strength of long-range Coulomb interactions. Interestingly, our matrix-RPA calculations indicate that there is a regime where the system can traverse from a magnetic phase to the SC phase by increasing the relative strength of long-range interactions compared to the on-site ones. These findings underscore the relevance of electron-electron interactions in shaping the intriguing properties of MATBG and offer a pathway for designing and controlling its SC phase.

In this article, we explore conditions of continuous emergent symmetries in gapless states, either as topological quantum critical points (TQCPs) or a stable phase with protecting symmetries and connections to smooth deformations of the gapped states around. For a wide class of gapless states that can be associated with fully isolated scale-invariant fixed points, we illustrate that there shall be emergent continuous symmetries that are directly related to smooth deformations of gapped states with symmetries lower than the protecting ones $G_p$. A short-distance invariance of gapped states under deformations can descend to be an emergent continuous symmetry when approaching the gapless limit. Around one TQCP with $G_p=Z_2^T$ symmetry, we construct these deformations explicitly and show emergence of symmetries via fully gapped quaternion superconducting states that break the protecting symmetry $G_p=Z_2^T$. For a 3D TQCP in DIII classes with $G_p=Z_2^T, U_{EM}=U\left(1\right)$, and $N_f=\frac{1}{2}$ fermions but without charge $U\left(1\right)$ symmetry, we further explicitly construct a corresponding boundary representation based on a $4\text{D}$ topological state with lattice symmetry $H=Z_2^T⋉U\left(1\right)$ and $N_f=1$ fermions. The lattice model is shown to be dual to a conventional $4\text{D}$ topological insulator. Although emergent continuous symmetries appear to be robust at weakly interacting TQCPs, we further show the breakdown of such one-to-one correspondence between deformations of gapped states and emergent continuous symmetries when gapless states become strongly interacting. In a strongly interacting limit, gapless states can be represented by a smooth manifold of conformal-field-theory fixed points rather than a fully isolated one. A smooth manifold of strong coupling fixed points hinders emergence of a continuous emergent symmetry in the strongly interacting gapless limit, as deformations no longer leave a gapless state or a TQCP invariant, unlike in the more conventional weakly interacting case. This typically reduces continuous emergent symmetries to a discrete symmetry originating from duality transformations under the protection symmetry $G_p$.

Proximity effect at superconductor/antiferromagnet (S/AF) interfaces, which manifests itself as generation of Néel-type triplet correlations, leads to sensitivity of the superconducting critical temperature to the mutual orientation of the AF Néel vectors in AF/S/AF trilayers, which is called the spin-valve effect. Here we predict that the spin-valve effect in AF/S/AF heterostructures crucially depends on the value of the chemical potential of the superconducting interlayer due to the occurrence of the finite-momentum Néel triplet correlations. In addition, we investigate equal-spin-triplet correlations, which appear in AF/S/AF structures for nonaligned Néel vectors of the AFs, and their role in the nonmonotonic dependence of the superconducting critical temperature of the AF/S/AF structure on the mutual orientation of the AF Néel vectors. The influence of impurities on the spin-valve effect is also investigated.

The distinctive hyperbolic properties of natural two-dimensional (2D) materials have garnered considerable attention in recent years due to their potential to surpass the limitations of metahyperbolic surfaces. It is essential to control hyperbolic regions and the sign of optical conductivities. This study introduces the concept of “bihyperbolicity” and establishes a critical connection between the semiconducting characteristics of 2D materials and their hyperbolic attributes. Through first-principles calculations, we illustrate the applicability of this strategy to materials such as the recently synthesized bismuth monolayer. The computations revealed that altering the type ($n$ type or $p$ type) of semiconducting bismuth monolayers can lead to a reversal of conductivity signs along two orthogonal directions, consequently enabling the precise regulation of hyperbolicity. The intriguing interplay between hyperbolicity and semiconductivity lays the foundation for crafting in-plane hyperbolic heterostructures using well-established semiconductor technologies. These heterostructures unlock a plethora of exotic optical phenomena, including negative refraction and negative reflection, thereby opening new horizons in optical engineering and device design.

We consider the hydrodynamic flow of an electron fluid in a channel formed in a two-dimensional electron gas (2DEG) with no-slip boundary conditions. To generate vorticity in the fluid, the flow is influenced by an array of micromagnets on the top of the 2DEG. We analyze the viscous boundary layer, and we demonstrate anti-Poiseuille behavior in this region. Furthermore, we predict a longitudinal voltage modulation, where a periodic magnetic field generates a voltage term periodic in the direction of transport. From an experimental point of view, we propose a method for a boundary-independent measurement of the viscosity of different electron fluids. The results are applicable to graphene away from the charge-neutrality point and to semiconductors.

Nontrivial bulk topological invariants of quantum materials can leave their signatures on charge, thermal, and spin transports. In two dimensions, their imprints can be experimentally measured from well-developed multiterminal Hall bar arrangements. Here, we numerically compute the low temperature ($T$) thermal (${\kappa }_{xy}$) and zero temperature spin (${\sigma }_{xy}^{sp}$) Hall conductivities, and longitudinal thermal conductance ($G_{xx}^{\mathrm{th}}$) of various prominent two-dimensional fully gapped topological superconductors, belonging to distinct Altland-Zirnbauer symmetry classes, namely $p+ip$ (class D), $d+id$ (class C), and $p\pm ip$ (class DIII) paired states, in mesoscopic six-terminal Hall bar setups from the scattering matrix formalism using kwant. In both clean and weak disorder limits, the time-reversal symmetry breaking $p+ip$ and $d+id$ pairings show half-quantized and quantized ${\kappa }_{xy}$ [in units of ${\kappa }_0={\pi }^2{k}_B^{2}T/\left(3h\right)]$, respectively, while the latter one in addition accommodates a quantized ${\sigma }_{xy}^{sp}$ [in units of ${\sigma }_0^{sp}=\hslash /\left(8\pi \right)]$. By contrast, the time-reversal invariant $p\pm ip$ pairing only displays a quantized $G_{xx}^{\mathrm{th}}$ at low $T$ up to a moderate strength of disorder. In the strong disorder regime, all these topological responses (${\kappa }_{xy}, {\sigma }_{xy}^{sp}$, and $G_{xx}^{\mathrm{th}}$) vanish. Possible material platforms hosting such paired states and manifesting these robust topological thermal and spin responses are discussed.

The rising interest in Dirac materials, condensed-matter systems where low-energy electronic excitations are described by the relativistic Dirac Hamiltonian, entails a need for microscopic effective models to analytically describe their transport properties. Specifically, for the study of quantum transport these effective models must take into account the effect of microscopic scale interfaces and the presence of well-defined edges, while reproducing the correct band structure. We develop a general method to analytically compute the microscopic Green's function of Dirac materials valid for infinite, semi-infinite, and finite two-dimensional layers with zigzag or armchair edge orientations. We test our method computing the density of states, scattering probabilities and topological properties of germanene and semiconducting transition metal dichalcogenides, obtaining simple analytical formulas. Our results provide a useful analytical tool with low computational cost for the interpretation of transport experiments on Dirac materials which could be extended to describe additional degrees of freedom like extra layers, superconductivity, etc.

Superlattice potential modulation can produce flat minibands in Bernal-stacked bilayer graphene. In this work we study how band topology and interaction-induced symmetry-broken phases in this system are controlled by tuning the displacement field and the shape and strength of the superlattice potential. We use an analytic perturbative analysis to demonstrate that topological flat bands are favored by a honeycomb-lattice-shaped potential, and numerics to show that the robustness of topological bands depends on both the displacement field strength and the periodicity of the superlattice potential. At integer fillings of the topological flat bands, the strength of the displacement field and the superlattice potential tune phase transitions between quantum anomalous Hall insulator, trivial insulator, and metallic states. We present mean-field phase diagrams in a gate voltage parameter space at filling factor $\nu =1$, and discuss the prospects of realizing quantum anomalous Hall insulators and fractional Chern insulators when the superlattice potential modulation is produced by dielectric patterning or adjacent moiré materials.

Recently, the quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ were observed directly. Motivated by this development, we reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. Derived from a three-dimensional $\mathit{k}·\mathit{p}$ model, it physically describes the top and bottom electronic surface states at the $\mathrm{\Gamma }$ point that become gapped due to the material's small thickness. However, we find that the four-band model for the surface states alone, as derived directly from the three-dimensional theory, is inadequate for the description of thin films of a few quintuple layers and even yields an incorrect topological invariant within a significant range of thicknesses. To address this limitation we propose an eight-band model which, in addition to the surface states, also incorporates the set of bulk states closest to the Fermi level. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the ${\mathbb{Z}}_2$ invariant in thin films of varying thickness. The band inversion around the $\mathrm{\Gamma }$ point, which endows the surfacelike bands with topology, is shown to be enabled by the presence of the additional bulklike states without requiring any reparametrization of the resulting effective Hamiltonian.

We show that in the proximity of $s$-wave superconductors, the magnetic topological surface states can transform into the Majorana surface state, featuring a single gapless Majorana cone with a parity anomaly when the superconducting pairing gap matches the surface magnetization gap. The emergence of an $N=1/2$ Majorana chiral edge current is observed at the boundaries between the gap region and the gapless region. Additionally, in systems with a single gapless Majorana cone, a quarter-quantized thermal Hall conductance appears under the dephasing. By mapping the system to a conductor-network model, we identify the appearance of 1/4 chiral heat channels as the cause of the quarter-quantized Hall thermal conductance. We observe the stability of this quarter-quantized thermal conductance under temperature variations, serving as a distinctive feature indicating the presence of a single gapless Majorana cone in the system. Our models can be experimentally realized using magnetic topological insulators or iron-based superconductors.

We investigate the effect of the twist angle on the proximity spin-orbit coupling (SOC) in $\mathrm{graphene}/{\mathrm{NbSe}}_2$ heterostructures from first principles. The low-energy Dirac bands of several different commensurate twisted supercells are fitted to a model Hamiltonian, allowing us to study the twist-angle dependency of the SOC in detail. We predict that the magnitude of the Rashba SOC can triple, when going from $\mathrm{\Theta }=0^{\circ }$ to $\mathrm{\Theta }={30}^{\circ }$ twist angle. Furthermore, at a twist angle of $\mathrm{\Theta }\approx {23}^{\circ }$ the in-plane spin texture acquires a large radial component, corresponding to a Rashba angle of up to $\mathrm{\Phi }={25}^{\circ }$. The twist-angle dependence of the extracted proximity SOC is explained by analyzing the orbital decomposition of the Dirac states to reveal with which ${\mathrm{NbSe}}_2$ bands they hybridize strongest. Finally, we employ a Kubo formula to evaluate the efficiency of conventional and unconventional charge-to-spin conversion in the studied heterostructures.

It has long been argued that the performance of organic bulk-heterojunction solar cells critically depends on the morphology of the active layer, a mixture of donor and acceptor materials in which the charge generation from sunlight occurs. In this work, optical homogenization principles are utilized to model the structure of the common active layer PM6:Y6. By systematically modifying the size and shape of Y6 acceptor inclusions within the morphology, we explore how these changes influence the refractive index and extinction coefficient of the resulting effective medium. A synergy of transfer matrix optical simulations with the Hecht equation is used to evaluate the effect of the inclusions features on the external quantum efficiency spectrum. The reported findings can be particularly helpful in the fabrication of similar classes of organic solar cells by indicating which aspects of active layer mixture may undermine the expected performance of the photovoltaic cells.

The direct bandgap found in hexagonal germanium and some of its alloys with silicon allows for an optically active material within the group-IV semiconductor family with various potential technological applications. However, there remain some unanswered questions regarding several aspects of the band structure, including the strength of the electric dipole transitions at the center of the Brillouin zone. Using the $\mathbf{k}·\mathbf{p}$ method near the $\mathrm{\Gamma }$ point, including 10 bands, and taking spin-orbit coupling into account, we obtain a self-consistent model that produces the correct band curvatures, with previously unknown inverse effective mass parameters, to describe 2H-Ge via fitting to ab initio data and to calculate effective masses for electrons and holes. To understand the weak dipole coupling between the lowest conduction band and the top valance band, we start from a spinless 12-band model and show that when adding spin-orbit coupling, the lowest conduction band hybridizes with a higher-lying conduction band, which cannot be explained by the spinful 10-band model. With the help of Löwdin's partitioning, we derive the effective low-energy Hamiltonian for the conduction bands for the possible spin dynamics and nanostructure studies and in a similar manner, we give the best-fit parameters for the valance-band-only model that can be used in the transport studies. Using the self-consistent 10-band model, we include the effects of a magnetic field and predict the electron and hole $g$ factor of the conduction and valance bands. Finally, we give an ellipticity analysis of the found effective mass tensor, to ensure the uniqueness of the solutions for its application to heterostructures.

In an intriguing recent experiment, it has been found that the two-dimensional (2D) surface states of a three-dimensional (3D) strong topological insulator (TI) support a nonzero Hall voltage transverse to an applied electric field even when the external magnetic field is in the plane (i.e., the in-plane Lorentz force vanishes). This so-called planar Hall effect (PHE) of TI surface states is found to be nonlinear, i.e., the Hall voltage scales quadratically with the applied electric field and linearly with the in-plane magnetic field. In this paper, we calculate the nonlinear PHE for strong topological insulator surface states with broken particle-hole symmetry and warping and provide results that interpolate continuously between the Dirac and normal fermion regimes, which can be compared with future experiments.